Question

The instantaneous values of current and voltage in an ac circuit are $I=100sin\left(314\right)t$ A and $E=200sin(314t+\frac{\pi }{3})V$ respectively. If the resistance is 1W then the reactance of the circuit will be

• A. $-200\sqrt{3}\Omega$
• B. $\sqrt{3}\Omega$
• C. $\frac{-200}{\sqrt{3}\Omega }$
• D. $100\sqrt{3}\Omega$

Answer 1

The correct option is B $\sqrt{3}\Omega$

$V_0=i_{o}Z\Rightarrow 200=100Z\Rightarrow Z=2\Omega$
Also $Z^2=R^2+X_L^2\Rightarrow (2{)}^2=(1{)}^2+X_L^2\Rightarrow X_L=\sqrt{3}\Omega$